The basic goal of this project is to advance understanding of change processes in children's thinking. The research incorporates a different conceptualization of change and different methods for studying it than have characterized most research in the field. The overlapping-wave model that underlies the research is based on the view that children typically possess multiple ways of thinking about a given phenomenon; that much of development involves changes in the relative frequencies of these alternative ways of thinking; that children choose adaptively among the alternatives; that they frequently generate new ways of thinking about given phenomena; and that generation of these new ways of thinking is constrained by domain-specific conceptual knowledge. The microgenetic methods that are used frequently within the research are based on densely sampling changing behavior as it is changing, with the goal of identifying the path, rate, breadth, variability, and sources of change. Such dense sampling of changing behavior provides a kind of high resolution microscope for indicating precisely how cognitive changes occur. The particular goals for the next 5 years are to 1) extend microgenetic methods to studying developmental differences in learning, 2) use the methods to compare problem solving in individual and collaborative contexts, 3) examine the impact on children's learning of their efforts to understand the reasoning underlying other people's reasoning, 4) assess how growing conceptual knowledge influences the new problem solving procedures that children generate, and 5) model the mechanisms that produce discovery of new strategies. The work promises to be of educational as well as theoretical importance, due both to the tasks being studied (geometry misconceptions, measurement, arithmetic, scientific reasoning) and many of the variables being investigated (effects of being asked to explain other people's reasoning, effects of calculus experience).